1. Field of the Invention
This invention relates to an electronic musical instrument, and more particularly to an electronic musical instrument for synthesizing musical notes by summing the products of multiplication of the nth powers of the fundamental frequency of a cosine wave and its coefficients A.sub.n.
2. Description of the Prior Art
Electronic musical instruments employing a digital system are indicated in U.S. Pat. No. 3,515,792 entitled "Digital Organ" and U.S. Pat. No. 3,809,786 entitled "Computor Organ". In the organ described in U.S. Pat. No. 3,515,792, the musical waveform required is sampled for one period, quantized and stored in a read-only memory. The stored waveform is repetitively read out by one or more clocks corresponding to the keyboard and multiplied or divided by an envelope waveshape stored in the read-only memory. In the organ set forth in U.S. Pat. No. 3,809,786, a discrete Fourier algorithm is implemented to compute each amplitude from a stored set of harmonic coefficients C.sub.n and a selected frequency number R. More in detail, the computations occur at regular time intervals independently of the waveshape period. In the waveshape computations carried out at regular time intervals, waveshape sample points qR (q=1, 2, 3, . . . ) are calculated by a note interval adder from the frequency number R corresponding to a key. For each sample point, W harmonics are read out by a harmonic interval adder and multiplied by harmonic coefficients C.sub.n characterizing the musical waveshape, by which C.sub.n (.pi.nqR/W), (n=1, 2, 3, . . . W) is calculated. During the above operation, attack, decay, release and other amplitude modulation effects are obtained by scaling the harmonic coefficients. The computations are all in real-time, so that the musical waveshape is obtained in real time.
While the conventional organs are quite useful they have some limitations. For example, in the organ of U.S. Pat. No. 3,515,792, the musical waveshape is stored in the read-only memory. On account of this, the stored content cannot be readily changed. In order to obtain a plurality of waveshapes, it is necessary to provide a number of memories respectively corresponding to the desired musical waveshapes. The organ of U.S. Pat. No. 3,809,786 is capable of synthesizing desired musical waveshapes and has some other advantages but, in this computer organ, computations are on real-time basis, so that a very high clock frequency is required. For example, in the case of generating a 32nd harmonic with respect to a sound having a scale frequency of up to 20.9KHz (C.sub.7), it is necessary to employ in the computer organ, for a single channel 4.29MHz. In a polyphonic tone synthesizing system in which the sound is time-divided by the employment of a single computation channel, the clock frequency is as high as 51.43MHz. As a result of this, integration of this circuit is difficult and inadvisable from the economical point of view.